A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget , x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-27x^2+1280x-7547

To find the maximum profit, we need to find the vertex of the parabola represented by the equation. The x-coordinate of the vertex can be found using the formula -b/2a, where a and b are the coefficients of the quadratic and linear terms, respectively. In this case, a = -27 and b = 1280.<br /><br />x = -b/2a = -1280/(-54) = 23.70<br /><br />Substituting this value back into the equation gives the maximum profit:<br /><br />y = -27(23.70)^2 + 1280(23.70) - 7547 = 7546.76<br /><br />Rounding to the nearest dollar, the maximum profit the company can make is $7547.